There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln({({x}^{2} + 1)}^{\frac{1}{2}}{\frac{1}{(x - 2)}}^{\frac{1}{3}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{(x^{2} + 1)^{\frac{1}{2}}}{(x - 2)^{\frac{1}{3}}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{(x^{2} + 1)^{\frac{1}{2}}}{(x - 2)^{\frac{1}{3}}})\right)}{dx}\\=&\frac{(\frac{(\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{1}{2}}})}{(x - 2)^{\frac{1}{3}}} + (x^{2} + 1)^{\frac{1}{2}}(\frac{\frac{-1}{3}(1 + 0)}{(x - 2)^{\frac{4}{3}}}))}{(\frac{(x^{2} + 1)^{\frac{1}{2}}}{(x - 2)^{\frac{1}{3}}})}\\=&\frac{x}{(x^{2} + 1)} - \frac{1}{3(x - 2)}\\ \end{split}\end{equation} \]

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